(1+1)维的具有时间与空间色散的五阶方程
PDF下载 (197)杨林燕,季 泳*.(1+1)维的具有时间与空间色散的五阶方程[J].宁波大学学报(理工版),2024,37(3):50-56.DOI:10.20098/j.cnki.1001-5132.2023.0705
YANG Linyan,JI Yong.(1+1) dimensional fifth-order equations with temporal and spatial dispersion[J].Journal of Ningbo University(Natural Science & Engineering Edition),2024,37(3):50-56.DOI:10.20098/j.cnki.1001-5132.2023.0705
| Title: | (1+1) dimensional fifth-order equations with temporal and spatial dispersion |
| 作者: | 杨林燕, 季 泳* |
| Author(s): | YANG Linyan, JI Yong |
| 关键词: | Hirota方法; 孤子解; 双线性Bäcklund变换; 行波解; 简化Hirota方法; bilinear Bäcklund transform |
| Keywords: | Hirota method; solitary solution; traveling wave solution; simplified Hirota method |
| 分类号: | O175.29 |
| DOI: | 10.20098/j.cnki.1001-5132.2023.0705 |
| 文献标识码: | A |
| 摘要: | 研究了一个新的(1+1)维的具有时空色散可积五阶方程, 推广了方程的形式, 并探讨了色散关系及其各自的系数情况. 利用简化Hirota方法推导了方程的可积条件, 导出了多孤子解. 此外, 利用指数型初始解构造方程的变换, 得出双线性方程, 继而利用Hirota双线性导数法导出单孤子解、双孤子解及N孤子解. 结合双线性方程给出了不同双线性交换算子的双线性Bäcklund变换, 继而导出不同条件下的双曲行波解、周期行波解等行波解. |
| Abstract: | In this paper, a new (1+1) dimensional equation with space-time dispersion integrable fifth-order equation is studied, the form of the equation is generalized, and the dispersion relationship and its respective coefficients are discussed. The integrable conditions of the equation are derived using the simplified Hirota method, and the multi-solution is also derived. In addition, the bilinear equation is obtained using the transformation of the exponential initial solution to construct the equation, and then the Hirota bilinear derivative method is used to derive the single solitary, double solitary and N solitary solution. The bilinear equation gives the bilinear Bäcklund transform of different bilinear exchange operators, and then the hyperbolic traveling wave solution and periodic traveling wave solution are derived under different conditions |
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| 备注/Memo: | 收稿日期: 2023−07−10. 宁波大学学报（理工版）网址: http://journallg.nbu.edu.cn/ 基金项目: 国家自然科学基金（12101340）. 第一作者: 杨林燕, 硕士研究生, 主要研究方向: 可积系统. E-mail: 2641708691@qq.com *通信作者: 季泳, 讲师, 主要研究方向: 动力系统及遍历理论. E-mail: imjiyong@126.com 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/ |
